Question

The sales of new products over time are found to follow a quadratic model before dropping off to zero at the end of the product’s lifetime. A new product is released with sales modeled by the equation
S
=
−
(
t
−
3
)
2
+
81
, where S represents the sales in millions of dollars and t represents the number of years the product will be sold. According to the equation, what will be the lifetime of this product?

Answer 1

The sales equation of the product is an illustration of a quadratic function, and the lifeline of the product is 12 years

How to determine the lifeline of the product?

The sales equation is given as:

S(t) = -(t - 3)² + 81

The lifeline of the product is when the sales hits 0.

This means that S(t) = 0

So, we have:

-(t - 3)² + 81 = 0

Subtract 81 from both sides

-(t - 3)² = -81

Divide both sides by -1

(t - 3)² = 81

Take the square root of both sides

t - 3 = 9

Add 3 to both sides

t = 12

Hence, the lifeline of the product is 12 years

#SPJ1

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